Nl230001621p

A frontal assessment battery at bedside
B. Dubois, MD; A. Slachevsky, MD; I. Litvan, MD; and B. Pillon, PhD
Article abstract—Objective: To devise a short bedside cognitive and behavioral battery to assess frontal lobe functions.Methods: The designed battery consists of six subtests exploring the following: conceptualization, mental flexibility, motorprogramming, sensitivity to interference, inhibitory control, and environmental autonomy. It takes approximately 10minutes to administer. The authors studied 42 normal subjects and 121 patients with various degrees of frontal lobedysfunction (PD, n ϭ 24; multiple system atrophy, n ϭ 6; corticobasal degeneration, n ϭ 21; progressive supranuclearpalsy, n ϭ 47; frontotemporal dementia, n ϭ 23). Results: The Frontal Assessment Battery scores correlated with theMattis Dementia Rating Scale scores (rho ϭ 0.82, p Ͻ 0.01) and with the number of criteria (rho ϭ 0.77, p Ͻ 0.01) andperseverative errors (rho ϭ 0.68, p Ͻ 0.01) of the Wisconsin Card Sorting Test. These variables accounted for 79% of thevariance in a stepwise multiple regression, whereas age or Mini-Mental State Examination scores had no significantinfluence. There was good interrater reliability (␬ ϭ 0.87, p Ͻ 0.001), internal consistency (Cronbach’s coefficient alpha ϭ0.78), and discriminant validity (89.1% of cases correctly identified in a discriminant analysis of patients and controls).Conclusion: The Frontal Assessment Battery is easy to administer at bedside and is sensitive to frontal lobe dysfunction.
Assessing frontal lobe function and thus being able
and patients with various degrees of executive dys-
to identify a dysexecutive syndrome are helpful for
function, and 3) interrater reliability.
the diagnosis and prognosis of brain diseases such asfrontotemporal dementias1 and for evaluation of the
Methods.Description of the Frontal Assessment Battery
severity of brain injuries. It can also help to identify
According to current theories, the frontal lobes
vascular dementias2 and parkinsonian disorders,
control conceptualization and abstract reasoning, mental
particularly progressive supranuclear palsy (PSP), in
flexibility, motor programming and executive control of ac-
which the presence of frontal lobe dysfunction sup-
tion, resistance to interference, self-regulation, inhibitory
ports the diagnosis.3 It may also be useful for differ-
control, and environmental autonomy.6,10-14 Each of these
entiating between degenerative disorders involving
processes is needed for elaborating appropriate goal-
subcortical structures and for evaluating the pro-
directed behaviors and for adapting the subject’s response
to new or challenging situations—functions that are medi-
The functions of the frontal lobes are difficult to
ated by the prefrontal cortex. For that reason, the designed
assess clinically. There is no test that reliably identi-
battery consists of six subtests, each exploring one of theaforementioned functions related to the frontal lobes.
fies a dysexecutive syndrome.5 In practice, extensive
Moreover, these subtests were chosen because the score of
neuropsychological batteries are needed to assess the
each of them significantly correlated with frontal metabo-
frontal lobe processes.6,7 Given the modular func-
lism, as measured in terms of the regional distribution of
tional organization of the frontal lobes,8,9 searching
18-fluorodeoxyglucose in a PET study of patients with
for a possible dysexecutive syndrome requires time-
frontal lobe damage of various etiologies.9 The processes
consuming tests exploring functions associated with
studied and the corresponding subtests of the FAB are
different frontal areas. Therefore, there is a need for a
presented below. The content, instructions and scoring of
brief tool exploring different domains of executive func-
each subtest are provided in the Appendix. The total scores
tion that are impaired in several neurologic diseases.
are calculated by adding the notes of the six subtests. The
We devised a bedside battery to assess the pres-
overall duration of the battery is approximately 10
ence and severity of a dysexecutive syndrome affect-
ing both cognition and motor behavior, and toevaluate it for 1) content and concurrent validity, 2)
1. Conceptualization: Abstract reasoning is impaired in
discriminant validity, comparing normal controls
frontal lobe lesions.11 This function is currently investi-
See also pages 1601, 1609, and 1613
From INSERM EPI 007 and Fédération de Neurologie (Drs. Dubois, Slachevsky, and Pillon), Hôpital de la Salpêtrière, Paris, France; and CognitiveNeuropharmacology Unit (Dr. Litvan), Henry M. Jackson Foundation, Bethesda, MD.
Supported by INSERM. Funded by a grant from Mideplan-Chile (A.S.).
Received June 12, 2000. Accepted in final form September 13, 2000.
Address correspondence and reprint requests to Dr. Bruno Dubois, Fédération de Neurologie, Hôpital de la Salpêtrière, 47 Boulevard de l’Hôpital, 75651Paris cedex 13, France; e-mail: [email protected]
Copyright 2000 by AAN Enterprises, Inc.Table Study group characteristics
Values are presented as mean Ϯ SD. Significantly different at p Ͻ 0.05 for: acontrols and patients; bfrontotemporal dementia (FTD) andcorticobasal degeneration (CBD) patients; cPD and CBD patients; dprogressive supranuclear palsy (PSP) and CBD patients; eFTD andmultiple system atrophy (MSA) patients; fPSP and MSA patients; gPD and PSP patients; hFTD and PSP patients; iPD and FTD pa-tients; jPD and MSA patients.
MMSE ϭ Mini-Mental State Examination; DRS ϭ Dementia Rating Scale; FAB ϭ Frontal Assessment Battery.
gated by card-sorting tasks, proverb interpretation, or
tend to execute echopractic movements, imitating the
similarities.15 The last task is easier for bedside assess-
ment and scoring. Subjects have to conceptualize the
Inhibitory control: Withholding a response may be
links between two objects from the same category (e.g.,
difficult for patients with damage to the ventral part of
an apple and a banana). Patients with frontal lobe dys-
the frontal lobes.21 In tasks anticipated to elicit a false-
function may be unable to establish an abstract link
alarm motor response, these patients are often unable
between the items (i.e., fruit), adhering to the concrete
to inhibit inappropriate responses.22 This difficulty in
aspects of objects (i.e., both are yellow), or may be un-
controlling impulsiveness can be assessed with the
able to establish a link of similarity (i.e., one is round
go–no go paradigm,23 in which the subjects must inhibit
a response that was previously given to the same stim-
2. Mental flexibility: Patients with frontal lobe lesions are
ulus, e.g., not tapping when the examiner taps twice.
specifically disturbed in nonroutine situations in which
Environmental autonomy: Patients with frontal lobe
self-organized cognitive strategies have to be built
lesions are excessively dependent on environmental
up.16,17 Literal fluency tasks are unusual, require self-
cues.24 Sensory stimuli can activate patterns of re-
organized retrieval from semantic memory, and are
sponses that are normally inhibited in normal controls.
easy to score. Frontal lesions, regardless of side, tend to
For example, the patient conceives the sight of a move-
decrease verbal fluency, with left frontal lesions result-
ment as an order to imitate (imitation behavior); the
ing in lower word production than right frontal le-
sight of an object implies the order to use it (utilization
sions.18 In this task, subjects need to recall as many
behavior); and the sight or sensory perception of the
words as they can beginning with a given letter in a
examiner’s hands compels the patient to take them
(prehension behavior). In some cases, the patients can
3. Motor programming: Patients with frontal lobe lesions
elicit these behaviors even if they have been explicitly
are also impaired in tasks requiring temporal organiza-
told not to do so. These abnormal behaviors (the sponta-
tion, maintenance, and execution of successive ac-
neous tendency to adhere to the environment) express
tions.12,13,19 In Luria’s motor series, such as “fist–palm–
the lack of inhibition normally exerted by the prefrontal
edge,” less severely impaired patients are unable to
cortex on the activation of patterns of behavior trig-
execute the series in correct order, whereas the most
severely affected are unable to learn the series. Simpli-fication of the task (two gestures instead of three) and
Subjects gave informed written consent to
perseveration (inappropriate repetition of the same ges-
participate. Forty-two normal control subjects (mean Ϯ
SD; age, 58 Ϯ 14.4 years), without any neurologic or psy-
Sensitivity to interference: Deficits in behavioral self-
chiatric history, were included (table). All control subjects
regulation may be observed in tasks in which verbal
had a Mattis Dementia Rating Scale (DRS)25 score Ͼ136 or
commands conflict with sensory information. This oc-
a Mini-Mental State Examination (MMSE)26 score Ͼ27.
curs in the Stroop test, in which the subject must name
To evaluate the discriminative power of the FAB, 121
the colors of words while inhibiting the natural ten-
patients with mild (PD, n ϭ 24; multiple system atrophy
dency to read the words. This also occurs in the case of
[MSA], n ϭ 6), moderate (corticobasal degeneration [CBD],
conflicting instructions, in which subjects must provide
n ϭ 21), or severe (frontotemporal dementia [FTD], n ϭ 23;
an opposite response to the examiner’s alternating sig-
progressive supranuclear palsy [PSP], n ϭ 47) frontal lobe
nal, e.g., tapping once when the examiner taps twice.
dysfunction27,28 were included (see table). All patients un-
Thus, subjects should obey verbal commands and re-
derwent an extensive clinical evaluation to confirm their
frain following what they see.20 Patients with a frontal
diagnosis and all met currently accepted diagnostic crite-
lobe lesion usually fail to obey the verbal command and
ria. The diagnostic criteria for PD were based on the pres-
December (1 of 2) 2000
ence of a parkinsonian syndrome with unilateral onset
the extent to which the six items of the FAB reflect the
characterized by a resting tremor or an akinetorigid syn-
same underlying construct, by calculating the Cronbach’s
drome, a good response to levodopa that persisted at the
time of evaluation, and the absence of exclusion criteria(e.g., supranuclear gaze palsy).29,30 The diagnostic criteria
Results.Technical properties of the battery.
for MSA included the presence of an extrapyramidal syn-
drome poorly responsive to levodopa, associated with an
FAB scores and the Mattis DRS performance in 121 pa-
autonomic or urinary dysfunction in the absence of exclu-
tients (r ϭ 0.82, p Ͻ 0.001). Similarly, the FAB scores
sion criteria.31 The diagnostic criteria for CBD included a
correlated with the number of criteria (r ϭ 0.77, p Ͻ 0.001)
slowly progressive asymmetric akinetorigid syndrome and
and perseverative errors (rho ϭ 0.68, p Ͻ 0.001) achieved
one or more of the following signs of cortical involvement:
in the Wisconsin CST. A stepwise multiple regression was
ideomotor apraxia, myoclonus, cortical sensory deficit, or
used to evaluate the influence on the FAB performance of
alien limb syndrome.32 The criteria for PSP included the
the following independent variables: age of patient, MMSE
presence of a gradually progressive disorder with an age at
and Mattis DRS scores, and the number of criteria and
onset of 40 years or later; a supranuclear limitation of
perseverative errors in the Wisconsin CST. The Mattis
vertical gaze; a prominent postural instability, with falls
DRS score and number of criteria achieved in the Wiscon-
occurring in the first year of symptom onset; and no evi-
sin CST accounted for 79% of variance in the FAB (F [2,82]
dence of another disease that could explain the symptoms;
ϭ 152.9; p Ͻ 0.001; r2 ϭ 0.79). Interestingly, age and
in the absence of exclusion criteria.33 The diagnosis of FTD
MMSE scores had no significant influence.
was based on a progressive onset of behavioral changes
fulfilling the Lund and Manchester criteria,1 a severe dys-
tween controls and patients after adjusting for age as a
executive syndrome on neuropsychological evaluation, and
covariate (analysis of covariance: F[1,131] ϭ 17. 24; p Ͻ
the absence of any other neurologic disorder sufficient to
0.001). The performance on the FAB correctly identified
explain the frontotemporal cortical deficit.1 The neuropsy-
89.1% of the cases (Wilke’s lambda ϭ 0.43, F[1,135] ϭ
chological evaluation of patients consisted of the MMSE26
176.2; p Ͻ 0.001). A stepwise discriminant analysis in pa-
and Mattis DRS for all patients,25 and the Wisconsin Card
tients with FTD and PSP using the six FAB subscores as
Sorting Test (CST)34 for 86 patients. The MMSE ranges
independent variables showed that similarities and pre-
were 30 to 24 for patients with PD, 30 to 21 for patients
hension behavior correctly classified 69.7% of the patients
with MSA, 30 to 13 for patients with CBD, 30 to 17 for
(Wilke’s lambda ϭ 0.865; ␹2 [ddl ϭ 2] ϭ 10.6; p ϭ 0.005).
patients with PSP, and 30 to 6 for patients with FTD.
subset of 17 patients with the FAB achieved an optimal
Technical properties of the battery.
interrater reliability (␬ ϭ 0.87, p Ͻ 0.001). The Cronbach’s
coefficient alpha between the items of the FAB of 121
the battery evaluates the existence of a frontal lobe syn-
patients was 0.78, suggesting good internal consistency.
drome,35 was analyzed by correlating the FAB total scorewith the patient’s performance on 1) the Wisconsin CST, atest considered to be sensitive to executive dysfunction36; and
Discussion.
2) the Mattis DRS, a global scale reported to be correlated
assessing frontal lobe function that could be applied
with the degree of executive dysfunction in neurodegenera-
by any practitioner, we designed a short assessment
tive diseases.4,25 For the Wisconsin CST, the number of crite-
battery, the FAB, based on our experience with focal
ria achieved and the number of perseverative errors were
frontal lobe lesions24 and movement disorders associ-
considered because both have been shown to be sensitive to
ated with striatofrontal dysfunction.4 Other tools
frontal lobe dysfunction.34 We performed a correlational va-
have already been designed to evaluate frontal lobe
lidity study because there is no “gold standard” that deter-
function at the bedside.38-41 A brief assessment of
mines the existence and severity of a frontal lobe syndrome.35
frontal and subcortical functions was proposed for
patients with suspected subcortical pathology, but
the FAB to discriminate between normal control subjects
patients with AD scored significantly lower on this
and patients with cognitive impairment according to the
scale than those with Huntington’s disease or PD.38
Mattis DRS scale. Patients without cognitive impairment
The EXIT 25, an executive interview, correlates not
were excluded for this analysis. Only 95 patients with a
only with tests sensitive to frontal lobe dysfunction
Mattis DRS score below 136 were included.
but also with the MMSE (r ϭ Ϫ0.85). This suggests
The ability of the FAB to differentiate the frontal dys-
function of patients with cortical and subcortical lesions
that the EXIT 25 is also sensitive to functions that
was studied by using a stepwise discriminant analysis in
are not executive.39 Another brief tool sensitive to
two groups of patients with frontal lobe dysfunction of
executive control, the CLOX (a clock drawing test),40
different origins—subcortical (47 patients with PSP) and
has been proposed, but only investigates one domain
of cognitive function: drawing. Lastly, Ettlin and
Kischka41 proposed the “frontal lobe score,” which is,
comparing the scores of two independent raters who were
however, not convenient for bedside assessment be-
present during the administration of the FAB by one of
cause it includes tasks such as the Trail-Making
them. Each rater was blind to the ratings made by the
Test and takes up to 40 minutes to complete. The
other. Interrater reliability was conducted in 17 patients
FAB is an easy test to administer, requires less than
and determined by calculating the kappa value.
10 minutes to complete, and is well accepted by pa-
We studied the internal consistency of the battery, i.e.,
tients. The six FAB subtests explore both cognitive
December (1 of 2) 2000
and behavioral domains under the control of the
Appendix
frontal lobes, each of them having been shown to be
Content, instructions, and scoring of the FAB
significantly correlated with frontal lobe metabolic
1. Similarities (conceptualization)
activity measured by 18-fluorodeoxyglucose using
PET scan.9 Moreover, each subtest is associated with
A banana and an orange (In the event of total failure: “they are
specific areas of the frontal lobes on the basis of
not alike” or partial failure: “both have peel,” help the patient bysaying: “both a banana and an orange are.”; but credit 0 for the
neuropsychological, electrophysiologic, and func-
item; do not help the patient for the two following items)
tional arguments: conceptualization with dorsolat-
eral areas,42,43 word generation with medial areas,44,45
and inhibitory control with orbital or medial frontal
Score (only category responses [fruits, furniture, flowers] are
areas.46,47 Therefore, performance on the six subtests
of the FAB can give a composite global score, which
evaluates the severity of the dysexecutive syndrome
and may suggest a descriptive pattern of executive
2. Lexical fluency (mental flexibility)
“Say as many words as you can beginning with the letter ‘S,’
The FAB presents good metric properties. The
any words except surnames or proper nouns.”
study demonstrated good internal consistency (Cron-
If the patient gives no response during the first 5 seconds, say:
“for instance, snake.” If the patient pauses 10 seconds, stimulate
bach’s alpha was 0.78),37 optimal interrater reliabil-
him by saying: “any word beginning with the letter ‘S.’ The time
ity (␬ ϭ 0.87), and concurrent validity. Indeed, the
FAB score was strongly associated with the perfor-
Score (word repetitions or variations [shoe, shoemaker], sur-
mance of patients on the Mattis DRS (rho ϭ 0.82)
names, or proper nouns are not counted as correct responses)
and Wisconsin CST (rho ϭ 0.77 for the number of
criteria), both of which evaluate different cognitive
functions under frontal lobe control. These functions
include initiation, conceptualization, and attention
3. Motor series (programming)
“Look carefully at what I’m doing.”
for the Mattis DRS scale25 and conceptualization and
The examiner, seated in front of the patient, performs alone
cognitive flexibility for the Wisconsin CST. Several
three times with his left hand the series of Luria “fist– edge–
recent studies have demonstrated that performance
palm.” “Now, with your right hand do the same series, first with
in the Wisconsin CST is related to functional activity
me, then alone.” The examiner performs the series three timeswith the patient, then says to him/her: “Now, do it on your own.”
in the prefrontal cortex.42,48-50 In contrast, the FAB
score is correlated neither with the MMSE score, a
Patient performs six correct consecutive series alone: 3
measure of more general cognitive function, nor with
Patient performs at least three correct consecutive series alone: 2
age (see the results of the stepwise multiple regres-
Patient fails alone, but performs three correct consecutive se-
sion). The battery also presents good discriminant
Patient cannot perform three correct consecutive series even
validity, allowing differentiation to be made between
control subjects and patients with frontal or subcor-
4. Conflicting instructions (sensitivity to interference)
ticofrontal cognitive impairment. However, the FAB
To be sure that the patient has understood the instruction, a
global score does not allow discrimination between
series of three trials is run: 1-1-1. “Tap once when I tap twice.” To
patients with predominantly subcortical (PSP) or
be sure that the patient has understood the instruction, a series of
cortical (FTD) dysfunction. Only two subtests dis-
three trials is run: 2-2-2. The examiner performs the followingseries: 1-1-2-1-2-2-2-1-1-2.
criminated between these patients to some extent—
prehension behavior (more severely impaired in
patients with PSP) and similarities (more severely
impaired in patients with FTD). This result is not
More than two errors: 1Patient taps like the examiner at least four consecutive times: 0
unexpected because patients with frontal and sub-
5. Go–No Go (inhibitory control)
corticofrontal lesions usually present similar cogni-
tive deficits and share only subtle neuropsychological
To be sure that the patient has understood the instruction, a
series of three trials is run: 1-1-1. “Do not tap when I tap twice.”To be sure that the patient has understood the instruction, a
Some points should be stressed, however. Test–
series of three trials is run: 2-2-2. The examiner performs the
retest reliability was not assessed. The anatomic cor-
following series: 1-1-2-1-2-2-2-1-1-2.
relation of the different subtests of the battery was
derived from data obtained with similar tests, but
not from the subtests themselves. Finally, although
highly significant correlations were shown between
Patient taps like the examiner at least four consecutive times: 0
the FAB and tests sensitive to frontal lobe functions,
6. Prehension behavior (environmental autonomy)
but not between the FAB and MMSE, it would be
The examiner is seated in front of the patient. Place the pa-
necessary to demonstrate that patients with non–
tient’s hands palm up on his/her knees. Without saying anything
frontal lobe injuries perform at a higher level than
or looking at the patient, the examiner brings his/her hands close
that observed for patients with frontal lobe injuries,
to the patient’s hands and touches the palms of both the patient’shands, to see if he/she will spontaneously take them. If the patient
to definitively consider the FAB as a measure of
takes the hands, the examiner will try again after asking him/her:
December (1 of 2) 2000
23. Drewe EA. Go–no go learning after frontal lobe lesions in
Patient does not take the examiner’s hands: 3
Patient hesitates and asks what he/she has to do: 2
24. Lhermitte F, Pillon B, Serdaru M. Human autonomy and the
Patient takes the hands without hesitation: 1
frontal lobes. Part I. Imitation and utilization behavior: a
Patient takes the examiner’s hand even after he/she has been
neuropsychological study of 75 patients. Ann Neurol 1986;19:
25. Mattis S. Dementia Rating Scale. Odessa, FL: Psychological
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Test. Neuropsychology 1999;13:135–143.Hippocampal and cortical atrophy predictdementia in subcortical ischemicvascular disease
G. Fein, PhD; V. Di Sclafani, MPH; J. Tanabe, MD; V. Cardenas, PhD; M.W. Weiner, MD; W.J. Jagust, MD;
B.R. Reed, PhD; D. Norman, MD; N. Schuff, PhD; L. Kusdra; T. Greenfield; and H. Chui, MD
Article abstract—Background: The cause of dementia in subcortical ischemic vascular disease (SIVD) is controversial.Objectives: To determine whether cognitive impairment in SIVD 1) correlates with measures of ischemic brain injury orbrain atrophy, and/or 2) is due to concomitant AD. Methods: Volumetric MRI of the brain was performed in 1) elderlysubjects with lacunes (L) and a spectrum of cognitive impairment—normal cognition (NCϩL, n ϭ 32), mild cognitiveimpairment (CIϩL, n ϭ 26), and dementia (DϩL, n ϭ 29); 2) a comparison group with probable AD (n ϭ 28); and 3) acontrol group with normal cognition and no lacunes (NC). The authors examined the relationship between the severity ofcognitive impairment and 1) volume, number, and location of lacunes; 2) volume of white matter signal hyperintensities(WMSH); and 3) measures of brain atrophy (i.e., hippocampal, cortical gray matter, and CSF volumes). Results: Among thethree lacune groups, severity of cognitive impairment correlated with atrophy of the hippocampus and cortical graymatter, but not with any lacune measure. Although hippocampal atrophy was the best predictor of severity of cognitiveimpairment, there was evidence for a second, partially independent, atrophic process associated with ventricular dilation,cortical gray matter atrophy, and increase in WMSH. Eight autopsied SIVD cases showed variable severity of ischemicand neurofibrillary degeneration in the hippocampus, but no significant AD pathology in neocortex. The probable ADgroup gave evidence of only one atrophic process, reflected in the severity of hippocampal atrophy. Comparison of regionalneocortical gray matter volumes showed sparing of the primary motor and visual cortices in the probable AD group, butrelatively uniform atrophy in the DϩL group. Conclusions: Dementia in SIVD, as in AD, correlates best with hippocampaland cortical atrophy, rather than any measure of lacunes. In SIVD, unlike AD, there is evidence for partial independencebetween these two atrophic processes. Hippocampal atrophy may result from a mixture of ischemic and degenerativepathologies. The cause of diffuse cortical atrophy is not known, but may be partially indexed by the severity of WMSH.
Subcortical ischemic vascular disease (SIVD) is char-
port risk of dementia to be higher among subjects
acterized by lacunar infarcts and deep white matter
with lacunar infarcts versus other subtypes of
changes. The proportion of vascular dementia (VaD)
stroke,4 and among patients with AD with concomi-
attributed to SIVD ranges from 36 to 50%, with
tant lacunar versus large-artery infarcts.5 Thus,
higher rates noted among African Americans1 and
SIVD is an important subtype of VaD either alone or
Asian Americans2 than whites.3,4 A few studies re-
From Neurobehavioral Research, Inc. (Dr. Fein and V. Di Sclafani); Psychiatry Research (Dr. Cardenas) and Magnetic Resonance Unit (Drs. Tanabe, Weiner,and Schuff, and L. Kusdra and T. Greenfield), Department of Veterans Affairs Medical Center; the Departments of Radiology (Drs. Tanabe, Cardenas,Weiner, Norman, and Schuff) and Psychiatry (Dr. Weiner), University of California, San Francisco; the Center for Functional Imaging (Dr. Jagust), LawrenceBerkeley Laboratory, the Department of Neurology (Drs. Jagust and Reed), University of California, Davis; and the Department of Neurology (Dr. Chui),University of Southern California, Los Angeles.
Supported by the National Institutes of Health (P01-AG12435, P50-AG10129, R01-AG10897), the State of California Department of Health ServicesAlzheimer Program, a National Research Service Award (DA-05683-02), and a Career Scientist Award (G.F.) from the Department of Veterans Affairs.
Received August 5, 1999. Accepted in final form October 2, 2000.
Address correspondence and reprint requests to Dr. Helena Chui, Geriatric Neurobehavior and Alzheimer Center, 800 Annex West, 7601 East ImperialHighway, Downey, CA 90242; e-mail: [email protected]
Copyright 2000 by AAN Enterprises, Inc.

“I tell you space is more plentiful than you think but it is far less substantial.” — David Duncan, “Occam’sRazor”H. J. KAMACK490 Stamford DriveNewark, DE 19711T. R. KEANE332 Spalding Rd. Wilmington, DE 19803With the aid of a small computer belonging to one of us, we have worked out many properties of the four-dimensional counterpart of Rubik’s Cube, which we call the Rubik Tesser